Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United StatesA.S. Barnes, 1885 - 512 من الصفحات |
طبعات أخرى - عرض جميع المقتطفات
عبارات ومصطلحات مألوفة
ABCD AC² adjacent angles altitude apothem Applying logarithms bisects centre chord circle circumference circumscribed cone consequently convex surface cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle inscribed intersection isosceles less Let ABC log sin lower base lune mantissa number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron principle demonstrated prism PROBLEM.-In PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment semi-circumference similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square straight line subtracting supplement Tang tangent THEOREM THEOREM.-Show tri-rectangular triangle ABC triangular prism triedral angle upper base vertex vertices volume whence
مقاطع مشهورة
الصفحة 28 - If two triangles have two sides of the one equal to two sides of the...
الصفحة 90 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
الصفحة 18 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
الصفحة 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
الصفحة 253 - For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...
الصفحة 61 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
الصفحة 94 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
الصفحة 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
الصفحة 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
الصفحة 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.